After just 16 appearances in a red shirt Strong's wish for more success came to fruition, as Liverpool won the FA Cup for the first time in the club's 73 year history. Strong, who was now used as a utility man, wore the number 4 jersey as the Reds beat Leeds United 2-1 after extra time in the Wembley final; it was also his first appearance in the competition for Liverpool, as he was deputising for the injured Gordon Milne. Unfortunately for Strong and the rest of the Anfield staff the Cup final joy was short-lived, as they lost to Inter Milan 4-3 on aggregate in the semi-final of the European Cup, having led 3-1 from the first leg Italy.

Strong went on to play in almost every outfield position over the next six seasons, but he eventually settled in at left back after Gerry Byrne hung up his boots. Strong was part of the side that won the 1965-66First Division championship, beating Leeds United into second by 6 points. He, however, missed the European Cup Winners Cup final, which Liverpool lost 2-1 to Borussia Dortmund at Hampden Park, through an injury that he picked up in the semi-final second leg win over Celtic. Strong had a major influence in the Reds reaching their first ever European final, as it was he that scored the winner, a towering header, even though he was carrying a leg injury.

Liverpool then went trophyless for a few seasons after the 1966 title win, and following a 1-0 defeat at the hands of Second DivisionWatford in the 6th round of the 1969-70 FA Cup, Bill Shankly decided that changes had to be made; the old guard had to be replaced by a younger generation, Strong was one of the players that was caught up in the cull. After exactly 200 games and 33 goals Strong left Liverpool on 10 August1970 for Coventry City.